Consider a part of an interstellar molecular cloud, which is going to
form a star. Assume this cloud fragment has a diameter of 0.2 light-years,
a mass of 1 solar mass, and is rotating at a rate of one revolution per
million years. (These are reasonable numbers for the cloud that formed the
solar system.)
a) What is the rotational speed of the outer edge of this cloud fragment?
b) Assume the cloud fragment is pulled together by gravity until it has
a diameter of 100 AU, the size of the solar nebula, and that angular
momentum is conserved, or equivalently that Kepler's 2nd law is obeyed.
What is the rotational speed and period of the outer edge of the cloud
fragment once it is this small?
c) So far we have been following problem 2 on page 402. But can this
happen? What is the orbital speed, according to Newton's version of
Kepler's 3rd law, 50 AU from a 1 solar mass star? What is the escape
speed there?
d) Gravity cannot accelerate something up to a speed greater than escape
speed, but it seems that it would have had to in order to form the solar
system. This is a problem that has puzzled astronomers for a long time.
Can you suggest a possible solution to the problem?

Before the cloud fragment in problem 1 was pulled together, what was
its density, which is defined as its mass divided by its volume?
Assume the cloud fragment is spherical.
a) Express your answer in grams per cubic centimeter (the density of
liquid water).
b) How many hydrogen molecules per cubic centimeter is that?

The luminosity of the Sun (the amount of light power it emits) is given
in your book.
a) From that number and the distance of the Earth from the Sun,
calculate the solar constant, which is defined as the solar light power
hitting a square meter at the Earth.
b) Compare the solar constant to the amount of light power hitting an area
of one square meter at a distance of 1 meter from a 100 Watt light bulb.

Your body generates heat from the food you eat at a rate of about 100
Watts. Calculate the power you generate per kilogram of mass to the power
that the Sun generates per kilogram of its mass. If you don't want to use
your mass, you can use mine, 66 kg.